We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally represents relationships in the data. We provide exact and approximate solutions to the decoding problem via constrained optimization, split relabeling, and nearest neighbors regression. These methods effectively invert the compression pipeline, establishing a map from the embedding space back to the input space using splits learned by the ensemble's constituent trees. The resulting decoders are universally consistent under common regularity assumptions. The procedure works with supervised or unsupervised models, providing a window into conditional or joint distributions. We demonstrate various applications of this autoencoder, including powerful new tools for visualization, compression, clustering, and denoising. Experiments illustrate the ease and utility of our method in a wide range of settings, including tabular, image, and genomic data.

A recent line of work has reframed individual decision trees as linear models on engineered features associated with their splits, opening routes for oracle inequalities and featureimportance reinterpretation, but leaving open the question of what unified geometric object a forest induces when one indexes its feature map by nodes rather than by splits. The present paper studies that object. KPP indexes the feature map by the nodes of the forest, weighted by a path metric that turns each coordinate into a component of a squared-Euclidean pathisometric embedding. KPP unifies four pillars under a single node-indexed representation whose Gram is non-diagonal and carries a metric: prediction, exact additive attribution, deterministic Lipschitz robust radius in the KPP metric, and uniform Rademacher risk bounds for regression and classification under fixed, honest, or cross-fit conditioning. All probabilistic guarantees are conditional on the representation and are stated under three explicit conditioning regimes; the robust-radius guarantee is deterministic in the KPP metric rather than in a norm on the raw input. Conjectured fast-rate refinements for both regression and classification are stated as open problems and are not claimed as theorems.

Tabular data have been playing a vital role in diverse real-world fields, including healthcare, finance, etc. With the recent success of Large Language Models (LLMs), early explorations of extending LLMs to the domain of tabular data have been developed. Most of these LLM-based methods typically first serialize tabular data into natural language descriptions, and then tune LLMs or directly infer on these serialized data. However, these methods suffer from two key inherent issues: (i) data perspective: existing data serialization methods lack universal applicability for structured tabular data, and may pose privacy risks through direct textual exposure, and (ii) model perspective: LLM fine-tuning methods struggle with tabular data, and in-context learning scalability is bottle-necked by input length constraints (suitable for few-shot learning). This work explores a novel direction of integrating LLMs into tabular data through logical decision tree rules as intermediaries, proposing a decision tree enhancer with LLM-derived rule for tabular prediction, DeLTa. The proposed DeLTa avoids tabular data serialization, and can be applied to full data learning setting without LLM fine-tuning. Specifically, we leverage the reasoning ability of LLMs to redesign an improved rule given a set of decision tree rules. Furthermore, we provide a calibration method for original decision trees via new generated rule by LLM, which approximates the error correction vector to steer the original decision tree predictions in the direction of "errors" reducing. Finally, extensive experiments on diverse tabular benchmarks show that our method achieves state-of-the-art performance.

Algorithm configuration, which involves selecting algorithm parameters based on sampled problem instances, is a crucial step in applying modern algorithms such as SAT solvers. Although prior work has attempted to understand the theoretical foundations of algorithm configuration, we still lack a comprehensive understanding of why practical algorithm configurators exhibit strong generalization performances in real-world scenarios. In this paper, through the lens of machine learning theory, we provide an algorithm-dependent generalization bound for the widely used model-based algorithm configurators under mild assumptions. Our approach is based on the algorithmic stability framework for generalization bounds. To the best of our knowledge, this is the first generalization bound that applies to a model closely approximating practical model-based algorithm configurators.

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure called Boulevard that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance in only O(nd2) time with the Nystr om method. Numerical experiments verify the asymptotic normality and demonstrate that our algorithms perform well, do not require early stopping, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

Industrial retrofit planning depends on structured operational data rather than free text: planners must estimate whether a newly registered prototype will require a retrofit, which retrofit package it will need, and how long the work will take. We study an industrial dataset linking a prototype-registration system (284,271 vehicles) with a retrofit-management system (48,716 cleaned visits), and compare strong tabular machine learning baselines with three LLM-based strategies on row-serialized inputs: embedding features (Amazon Titan), direct prompted classification (Claude Sonnet 4), and an ML+LLM stacking approach. Across binary occurrence prediction, 15-way retrofit-type classification, per-visit duration regression, and an aggregated monthly benchmark, classical tree ensembles remain the strongest standalone models. However, the LLM results reveal a consistent pattern: embeddings remain useful on tables (binary AUC = 0.982), direct prompting collapses once semantic signal is stripped by hashing (binary AUC = 0.500; multiclass weighted F1 = 0.018), and hybrid stacking yields the best manually built multiclass model (weighted F1 = 0.626). On the monthly benchmark, lag-based machine learning outperforms time-series foundation models, though Chronos-small remains competitive in zero-shot forecasting. The results suggest that on privacy-constrained industrial tables, LLMs are more effective as complementary components than as replacements for strong tabular baselines.

The advent of Machine Learning as a Service (MLaaS) has heightened the trade-off between model explainability and security.

Autonomous spacecraft require rapid, lightweight, and reliable onboard detection of cyber-RF threats. Using the SPARTA attack model, we analyze the latency-accuracy trade-offs of TinyML-compatible classical models -- Random Forest, Logistic Regression, SVM, and MLP -- for detecting uplink jamming, Fake-NR spoofing, payload manipulation, ground-segment compromise, and unauthorized command injection. We present a physics-informed theoretical analysis of each model's computational complexity, VC dimension, Lipschitz continuity, and latency scaling, supported by empirical measurements on adversarial RF spectrograms generated via BandErasure, FakeNR, and NoiseBurst corruption modes. Results show that Logistic Regression achieves microsecond-level inference with only a 1\% accuracy drop relative to Random Forest, making it an effective TinyML baseline for onboard autonomy. The study also identifies opportunities for advancing spacecraft cybersecurity through richer feature encoders and multi-timescale learning architectures, building on recent progress in edge intelligence and trustworthy AI.

CART random forests are among the most widely used modern predictive methods, with well-documented empirical success. Yet, at the mechanistic level, the algorithm is often treated as a black box because of its complexity. In this paper, we develop a stochastic-control perspective on feature-subsampled CART random forests, named CART random opportunity-set allocation (CART-ROSA). At each node, the random subset of features is interpreted as a random feasible action set, and the CART split rule as a masked-action allocation policy. This policy induces a controlled stochastic process over informative split-count states, whose terminal law determines both single-tree error and cross-tree interaction terms in the forest mean squared error (MSE). Such representation opens the black box of CART-forests by separating two design levers: the informative-opportunity rate induced by feature subsampling, and the contraction strength from the within-mask split policy. We establish that the CART policy is locally stabilizing: it contracts imbalances in informative split allocations and concentrates terminal tree geometry. At the system level, however, it can be globally suboptimal for the forest objective. Specializing to the linear model, we derive the MSE risk expansion explicitly. Our results show how an operations-research perspective makes tractable a theoretical gap difficult to access from the standard algorithmic description of CART forests.

We develop a rigorous statistical theory of multi-head attention (MHA) as an ensemble of Nadaraya-Watson (NW) kernel regression estimators. Building on the algebraic identity between single-head softmax attention and the NW estimator, we prove that MHA is a structured ensemble of H NW estimators, each operating in a distinct learned projection subspace of the key space. We derive an explicit Bias-Variance-Covariance decomposition of the MHA mean squared error, showing that variance reduction depends not merely on the number of heads H but fundamentally on the decorrelation of head outputs. Decorrelation is governed by the principal angles between learned projection subspaces: orthogonal projections yield maximum variance reduction; aligned projections yield none. We introduce the Head Diversity Index (HDI), a computable spectral measure of inter-head decorrelation, and prove that MHA mean squared error is monotonically decreasing in HDI. This provides the first rigorous theoretical explanation for the empirically observed specialization of attention heads. Under a fixed total-dimension budget D = H * d_k, we solve the optimal head-dimension allocation problem, deriving the MSE-minimizing pair (H*, d_k*) from data distribution and regression smoothness. The solution yields a new architectural scaling law: the optimal per-head dimension grows logarithmically with training set size, while the optimal number of heads grows nearly linearly with the total budget D. Our framework unifies three strands of prior work: the NW theory of single-head attention, the general weighting theory for ensemble learning, and the decorrelation-variance-reduction isomorphism between biological and computational ensembles. Multi-head attention is the Transformer's instantiation of a universal principle: identical agents plus diversity-enforcing mechanisms yields emergent optimality.